Temper, Temper

Horrible Homework:
Q. Hydrogen and oxygen in a sample gas have the same temp. This means the hydrogen molecules, on average, have the same:
(a) speed, but less K.E.
(b) K.E., but more speed
(c) speed, but more K.E.
(d) speed and the same K.E.
(e) K.E. but less speed.

I have no idea how to approach this problem. I think it got stuck in our Chapter Review by mistake, but try telling my professor that. He has forbidden me to speak to him, anyway.

I can't get this one, either: If air were a better conductor than it is, at nighttime, the earth would be:
(a) considerably cooler
(b) considerable warmer

I can't figure it out, because surely, if the air were a better conductor than it is, it would have warmed the earth so much better during the day, and the thus the loss at night would not be enough to make it too much colder? But ignoring that, it would make it very much cooler, wouldn't it?

One final one: Nellie Newton pours herself a cup of very hot tea. Should she immediately put some spoonsful of ice water in it, or wait until she is just about to drink it, in order to get it cooled down the quickest?

That's just nuts. This is the kind of question that makes people hate physicists, this sort of nonsense. There's just too much open here. I'm SUPPOSED to answer that she should wait right until she wants to drink it, because it's the diff in the two temps that makes it cool at a faster rate. But we could be talking seconds. Maybe she wants to dump it in right away and start sucking it down. I mean, if she puts the water in it right away, seconds after it's poured, the temp diff would be greatest at THAT point and it would cool down fast. While she's waiting around to drink it and waiting to put the ice water in, it's cooling, right? Then it won't go as fast. Aw, it's a bunch of hooey, that kind of question.

H is lighter than O. What has that to do with the molecules running about? Can't they be even?

Conductor of HEAT, I guess, because we are in a chapter about thermal energy and change of phase. So, the question asks about if the earth would cool down or warm up if the air were a better conductor (of heat) at night...

Nellie Newton wants to cool down the tea. Should she pour the cool spoons of water in it right off or wait until she wants to take her first sip?

Do you see why that question has me so mad? We can't know Nellie's mind. We can't know if she's going to stir it. We can't know if she wants to sip it in five minutes or in six minutes. But the ANSWER is supposed to be that she should wait to pour it in right before she wants to drink it. He gave the answer, we're supposed to figure out why that makes sense. It doesn't make sense. It's one of those inside jokes physicists tell one another. Hmph.

What has that to do with the molecules running about? Can't they be even?

The critical thing is that the product of (1/2)mv^2 be the same for both species, and so if m is less for one, v has to be greater for that one. Has equipartition of energy come up as a topic in your class?

In order for H2 molecules to have the same amount of energy as O2 molecules, they must be moving faster, precisely because they are less massive. Going the same speed gives H2 molecules less energy than it does O2 molecules. By the way, don't use 1/2mv^2 for the kinetic energy of molecules... It's not correct but you kinda get the idea.

I'd argue it'd be a cooler place. Heat wants to escape into space (space is cold), so the more conductive the earth is, the more it will allow it to.

For the third one, I'm still really not sure what it's asking, but I think it's arguing that energy will escape the cup of tea into the ambient air when the cold water is not added, whereas adding the cold water will decrease the energy of the tea by a set amount and interfere with the tea cooling via the air. So therefore it you let as much escape into the air as possible, you're starting for a lower baseline and the cold water's effects are that much more prominent.

*The H molecules, while zippier, cannot hit as hard as the larger, slower O molecules. Hmmm. And I shouldn't use the nice equation you gave. Got it.

*The earth will get cooler, much cooler. Check.

*Nellie ought not put the cool water in until she is ready to drink it, because that would interfere with the air cooling it down. Makes zero sense to me, as I felt the biggest cool-down would be when the two liquids were very different temps, but I will memorize it and regurgitate it at the proper time. Who waters down their tea, anyway?

One final one: Nellie Newton pours herself a cup of very hot tea. Should she immediately put some spoonsful of ice water in it, or wait until she is just about to drink it, in order to get it cooled down the quickest?

It depends on how long she wants to wait. If she plans on drinking it like 10 minutes later, it would be best to let it sit and put the ice in after. If she wants to drink after less time it takes the ice to melt, she should put the ice in immediately.

Staff: Mentor

Newton's Law of Cooling

holly said:

One final one: Nellie Newton pours herself a cup of very hot tea. Should she immediately put some spoonsful of ice water in it, or wait until she is just about to drink it, in order to get it cooled down the quickest?

I suppose they want you to apply your knowledge of Newton's law of cooling (Nellie's great-granddad?) which states that hot things lose heat faster than cool things. So the hot tea will cool off quicker if she waits until the last possible second to put in the ice water.

Thank you all for your words of wisdom. Not to sound as dumb as I might perhaps be, but there is also a question of Nellie pouring herself some COFFEE and then the bit about waiting to put the CREAM in it. I suspected it was a trick question, having to do with getting sick because she let the cream sit around, or perhaps it was HEATED cream, but that was what made my prof say I am too hyper, give him headaches, etc etc and to kindly shut up for the rest of the semester. But I see now that it was just the same question as the TEA question, which I do not understand but I'm memorizing ALL the remarks so that I can put it all down at for the essay question. So I'm at the mercy of the board now. We have five more chapters. I'm kind of proud that through fear of annoying the homework board, I actually figured out almost all the questions myself this time. The hard ones you guys get.